5. Rheological properties of hydrate suspensions in an asphaltenic crude oil

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Rheological Properties of Hydrate Suspensions in an Asphaltenic Crude Oil
Conference Paper · May 2002
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Rheological Properties of Hydrate Suspensions in an Asphaltenic Crude Oil
Ricardo Camargo (1) , Thierry Palermo (2) *
(1)
Petrobras (Brazil); (2) Institut Français du Pétrole (France)
Rheological properties of hydrate suspensions in an asphaltenic crude oil were investigated. Two
different experimental devices were used: a laboratory scale P-T cell adapted as a double coaxial
cylinders rheometer and a 2” x 140 m flow loop. Hydrate suspensions exhibit shear thinning behavior
and thixotropy, which can be interpreted as the result of a weak flocculation process between hydrate
particles. A rheological model has been developed. In this model, the viscosity of the suspension is
related to the size of aggregates, resulting from the balance between attractive forces and shear
stresses. By comparison with experimental results, an estimation of the magnitude of attractive forces
between hydrate particles is given. The origin of these forces is discussed.
1. Introduction
When gas hydrates formation takes place in gas or oil
production flow lines, hydrate plugs might form, leading
to a complete blockage. A common practical process to
remove such plugs consists in depressurizing or
eventually heating the line to enable hydrate crystals to
dissociate. In addition to safety hazards associated with
these methods (Sloan, 2000) deep offshore oil production
conditions makes their deployment difficult or
impossible to achieve. Consequently, technical solutions
rather consist in preventing hydrate plugs formation by
insulating the lines or injecting chemicals. Mainly for
economical reasons, insulation is today preferred for oil
production by most of oil companies.
In addition to standard prevention methods, the intrinsic
capability of some crude oils to transport hydrate
particles is today also seen as an interesting potential
option. In the past, it was shown that chemicals, named
dispersant additives, enable a stable W/O emulsion to
form and then, once hydrate formation has occurred,
allows the transportation of hydrates as a suspension of
hydrate particles in the oil phase (Palermo et al., 1997).
Polar compounds contained in crude oils, such as
asphaltenes, are known to promote stable W/O emulsions
(Førdedal et al., 1996) and are also suspected to further
hydrates transportation (Leporcher et al., 1998).
In this work, hydrate suspensions were formed in an
asphaltenic crude oil under shear flow conditions. Their
rheological properties were investigated with the help of
two different devices: a laboratory scale P-T cell adapted
as a double coaxial cylinders rheometer and a 2” x 140 m
flow loop. In former papers (Camargo et al., 1999, 2000,
2001), results were presented and showed that such
*
Corresponding author. E-mail: [email protected]
hydrate suspensions exhibited shear-thinning behavior
and thixotropy which can be interpreted as the result of a
weak flocculation process between hydrate particles.
In this paper, we present a rheological model, which
relates the viscosity of the suspensions to the size of
aggregates, resulting from the balance between attractive
forces and shear stresses. By comparison with
experimental results, an estimation of the magnitude of
attractive forces between hydrate particles is given. The
origin of these forces is discussed.
2. Experimental Devices
Rheological Cell. The P-T rheological cell is able to
work at a pressure of up to 9 MPa and with temperatures
ranging from -15 to 65°C. It has a double coaxial
cylinders geometry and works with imposed shear rate
(or angular velocity) and measured torque. The angular
velocity of the mobile cylinder ranges from 0 to 70 rad/s,
while the torque is limited to 35 mN.m. The experimental
procedure consisted in initially filling the cell with a
W/O emulsion prepared as described in section 4. The
pressure was then increased up to the working pressure
(P=8 MPa). Hydrate formation was achieved by keeping
the temperature at a fixed value inside the hydrate region
(T=7.5°C) under shear conditions corresponding to a
moderate angular velocity of 35 rad/s. Rheological
behavior of the suspension was then investigated by
varying the angular velocity and measuring the
associated torque. A thorough description of this
experimental device is given by Camargo et al. (1999).
Flow loop. The so-called “Lyre” loop, located at the IFP
research center in Solaize, is 140 m long with an internal
diameter of 2" and was designed to study “Flow
Assurance” issues under multiphase flow conditions. The
working temperature ranges from 0 to 50°C and the
maximum pressure is 10 MPa. Fluid circulation is
ensured by a positive displacement pump, that minimizes
possible crushing of solid particles, for the liquid phase,
and by a membrane compressor for the gas phase. More
details about the Lyre loop can be found in reference
(Palermo and Maurel, 2000). Emulsion was formed
under pressure and multiphase flow conditions. Hydrate
formation was achieved by cooling the fluids at a
temperature lower than 5°C, at a constant pressure of 7.5
MPa at the outlet extremity of the flow line. Rheological
behavior of the suspension was then investigated at a
temperature of 7.5 °C under liquid flow conditions
(Camargo et al., 2000).
3. Fluids composition
The crude oil comes from a Brazilian deep-water field
and was provided by Petrobras. The main properties of
the dead crude oil in terms of viscosity, density and
SARA analysis are given in Table 1. Asphaltenes are
defined as the n-heptane insoluble fraction of the oil.
Density at 15 °C
kg/m3
914
Viscosity at 20 °C
cp
135
Saturates
% weight
50 1
Aromatics
% weight
30 1
Resins
% weight
15 2
Asphaltenes
% weight
5 1
Table 1: Properties of the dead crude oil
Viscosity of the live crude oil (dead crude oil saturated
with gas under pressure) is given in Table 2.
T = 7.5 °C
T = 12 °C
T = 25 °C
60 10
44 5
20 2
0 (cp)
Table 2: Viscosity of the live crude oil at P=7.5 MPa
In the rheological cell, the gas phase was composed of
90% molar of methane and 10% molar of ethane. In the
flow loop, the gas phase was a natural gas delivered from
the gas network. The molar fractions were typically in
the range 92%-95%, 3%-5% and >1% for C1, C2 and
C3+, respectively. In both cases, structure II hydrates are
expected to form. However, coexistence of structure II
and structure I may exceptionally be encountered
depending on pressure and temperature conditions
(Ballard and Sloan, 2001).
The water phase was salted water (33 g/l NaCl).
4. Emulsion Stability
W/O emulsions were investigated under ambient
conditions (atmospheric pressure, temperature of 20 °C).
They were prepared by agitating the dead crude oil with
a high shear mixer Ultra-Turrax T25 running at 8,000
rpm for 180 seconds, while slowly pouring the water on
it. Three water contents: 15 wt%, 30 wt% and 50 wt%,
were investigated. Observation, focused on the
appearance of a free water phase, indicated that
emulsions remained very stable over a period of several
months.
Emulsions were also prepared, at a water content of 30
wt%, with three fractions removed from the crude oil:
saturates + aromatics, resins and asphaltenes. For the oil
containing only saturates and aromatics, the emulsion is
not stable and a free water phase was rapidly visible,
leading to a complete phase separation after some
minutes. For the oil phase corresponding to 1wt% of
resins in toluene, a small quantity of free water phase
appeared after some minutes. For the last system, 1 wt%
of asphaltenes in toluene, a stable emulsion was formed
and no free water was visible after a period of several
days. That confirms, for the crude oil investigated in this
study, that asphaltenes are the major oil components
acting as natural surfactants.
Size of water droplets was determined by optical
microscopy. Droplet diameters have been measured in
the range of 0.5 to 3 m. Size of water droplets was also
determined for emulsions sampled from the rheological
cell and the flow loop, before hydrate formation as well
as after hydrate dissociation. No significant change in
size has been noticed.
5. Rheological Behavior of Hydrate Suspensions
The crude oil showed a very good capability in
transporting hydrate particles as a suspension and made
rheological investigations feasible. As presented in
previous papers (Camargo et al., 1999, 2000), shearthinning and time-dependant (thixotropy) properties
were observed for hydrate suspensions for a volume
fraction of 0.27 and above. On the other hand,
suspensions formed at a volume fraction of 0.134
behaved roughly like a Newtonian system.
Shear-thinning behavior is frequently observed for
concentrated suspensions. This phenomenon, particularly
when it is associated with a thixotropic behavior, is
generally attributed to a reversible aggregation process
that takes place between particles under shear flow. The
main questions therefore concern the type of force of
interaction involved in this aggregation process, as well
as its order of magnitude.
In the following, a phenomenological model is proposed
to explain the non-Newtonian behavior of hydrate
suspensions formed with this crude oil.
6. Phenomenological Model
Basic Assumption. Hydrate crystals are expected to
form at the water-oil interface. Thus, a solid shell forms
around water droplets making them behave as solid
particles. In the following, hydrate particles will be
assumed to be spherical, with an identical diameter as
water droplets.
Viscosity of concentrated suspensions. Numerous
equations have been developed in order to relate
viscosity of concentrated dispersions to particle
concentrations. These equations are generally expressed
as a relationship between the relative viscosity r and the
couple (
max). The relative viscosity is the ratio
between the apparent viscosity of the suspension and
the viscosity of the dispersing liquid 0. is the particle
volume fraction and max is physically interpreted as the
maximum volume fraction to which particles can pack.
In this work, we will use the equation proposed by Mills
(1985), well adapted to hard spheres of equal size and
accounted only for hydrodynamic interactions:
1
Eq. 1
µr
; max 4
2
7
1
considering a mechanism of destruction based on the
erosion of microflocs (Mühle, 1993), the maximum size
of aggregates for laminar flow is given by:
Eq. 5
where
Viscosity of concentrated aggregated suspensions.
Several theoretical models have been proposed in the
literature to describe the growth of particle clusters either
by perikinetic aggregation (caused by Brownian motion)
or by orthokinetic aggregation (caused by medium flow)
(Jullien, 1990; Potanin, 1990). The porosity of the
resulting aggregates is taken into account by introducing
a fractal dimension f, relating the number of particles N
per fractal aggregate to characteristic lengths of the
system (dA: aggregate diameter; dp: particle diameter):
N
dA
dp
Due to the fractal structure of aggregates, it has been
proposed that an effective particle volume fraction eff
should be considered instead of the real volume fraction
in the expression for the viscosity (Mills, 1985):
1
eff
Eq. 3
µr
; max 4
2
7
eff
1
max
with
3 f
Eq. 4
eff
1
4 f
µ0
In Eq. 5, the shear stress exerted to aggregates is related
to the viscosity 0 of the dispersing liquid. It is only
correct when aggregates do not interact, i.e.,
0.
However, for finite , hydrodynamic interaction of
aggregates can be taken into account, as proposed by
Potanin (1990), by substituting in Eq. 5 the viscosity 0
by the apparent viscosity of the suspension . Finally, we
have:
1
Eq. 6
Fa d p
d A, max
2 f
4 f
µ
At the equilibrium, we consider that dA
dA,max.
Combining Eq. 3, Eq. 4 and Eq. 6, dA/dp can be
determined by solving the following equation:
Eq.7
dA
4 f
dp
Fa 1
2
dp µ 0 1
dA
max
dA
3 f
2
dp
3 f
0
dp
If the solution of Eq.7 is dA/dp <1, dA is fixed equal to dp.
The relative viscosity is then determined by using Eq. 1.
7. Results
f
Eq. 2
d A,max
2 f
is the shear rate.
max
max is taken as the packing concentration of randomly
packed spheres of same diameter.
Fa d p
dA
dp
It is well accepted that the fractal dimension, for
perikinetic aggregation , ranges from about 1.7 to 2.1.
Under shear conditions, it is generally reported that
aggregates are more compact with fractal dimension
larger than 2 and up to 2.7 (Hoekstra et al, 1992).
Because of viscous forces applied on aggregates in the
flow, they cannot growth indefinitely. A maximum size
is reached depending on the balance between the shear
stress and the force of adhesion Fa between particles. By
Comparison between model and experiment. Results
obtained from the phenomenological model are
compared in with some experimental results obtained for
hydrate suspensions formed with the asphaltenic crude
oil.
Except for the force of attraction Fa, all the parameters
have been set to their assumed or measured value.
According to the discussions above, the fractal
dimension has been set to f = 2.5, the maximum packing
concentration to max = 4/7, and the particle diameter to
dp = 1.5 m. Recall that the viscosity of the continuous
oil phase at 7.5°C is 0 = 60 cP.
Experimental results are presented for two particle
volume fractions :
= 0.134 and
= 0.274. Higher
volume fractions were also investigated. However, as it
is frequently observed for suspensions at high volume
fraction, a slip effect has been experienced. This
phenomenon will not be discussed in this paper. Due to
time-dependant properties of suspensions, only results
obtained during the increase of the shear rate are shown.
Indeed, it is expected that the destruction of aggregates is
a more rapid process than formation. Consequently, the
relative viscosity measured under such conditions is
probably closer to the equilibrium state than the one
measured during a decrease of the shear rate.
Results of calculation presented in, correspond to a force
of attraction : Fa = 1.2 nN. Expressed with respect to the
radius of curvature of the surface R, we have Fa/R =1.6
mN/m, with R = dp/2.
reported. Corresponding experimental data obtained in
the loop for = 0.134 and 0.274 are also reported.
200
180
= 0.274
160
140
120
0
= 0.0706 Pa.s
= 57.66 Pa
100
40
80
35
60
40
30
= 0.274
25
0
= 0.0724 Pa.s
= 6.72 Pa
= 0.134
20
0
20
0
100
200
300
400
Shear Rate (1/s)
15
10
= 0.134
5
0
0
100
200
300
400
500
600
700
800
Shear rate (1/s)
Figure 1: Comparison between calculation and
experimental data obtained for hydrate suspensions in the
asphaltenic crude oil. Lines: calculated from the model;
marks: experimental data obtained in the loop ( ) and in
the cell (x).
Globally, the evolution of the relative viscosity with the
shear rate, depending on the particle volume fraction, is
well described by the aggregation model. At low volume
fraction ( = 0.134), calculation indicates that the
increase of the relative viscosity should be only
significant at low shear rates (below 50 s-1).
Experimentally, in the range of shear rates investigated
(50 to 600 s-1) neither shear-thinning nor thixotropic
behavior have been observed. At = 0.274, we have a
good agreement between calculation and experimental
data with the shear-thinning behavior well described.
Rheological behavior. As analytically demonstrated by
Mills (1985) in the particular case of a fractal dimension
f = 2, the rheological behavior of an aggregated
suspension can be described by a Casson’s like equation :
1
1
1
2
2
2
Eq. 8
0
where is the shear stress, 0 the yield shear stress, and
a function of Fa, dp, and
From the calculated viscosity, it is possible to deduce the
corresponding shear stress
. By fitting the
calculated values of with an equation of the form of Eq.
8, the yield shear stress 0, as well as , can be
determined. For simplicity,
has been taken as a
constant that depends only on the volume fraction.
Figure 2 shows results of such a calculation for the two
volume fractions
= 0.134, 0.274. Values of the
calculated yield shear stress 0 and the constant are
Figure 2: Rheological behavior of hydrate suspensions in
the asphaltenic crude oil. Corresponding Casson’s law
= 0.137 and 0.274. (O): theoretical values of
for
determined from the viscosity ; lines: fitted Casson’s
law; ( ): experimental loop data.
8. Forces of
particles
interaction
between
hydrate
Previous calculations have been performed with a force
Fa/R = 1.6 mN/m. For a better understanding of
physicochemical properties of hydrate suspensions, it is
interesting to know the origin of forces involved in
hydrate particles interaction for this system.
Stability of colloidal systems is often explained through
the well-known DLVO theory, which takes into account
the van der Waals forces and the electrostatic (or doublelayer) forces. Since, in our case, the continuous phase is
organic, it is expected that repulsion electrostatic forces
are negligible. On the other hand, van der Waals forces
(attractive forces for identical particles) always exist in
disperse systems.
The van der Waals forces between two spheres of same
radius R is given by the relation (Israelachvili, 1992a):
AR
Eq. 9
Fa
12D 2
where A is the Hamaker constant and D the distance
which separates the two spheres. The Hamaker constant
is related to the dielectric constant and the refractive
index n of the different media (explicit formula can be
found in Israelachvili, 1992a).
Let us set down for the hydrate phase:
58 (Makogon,
1997) and n 1.35 (Herri & Gruy., 1995), and for the
hydrocarbon liquid phase:
2 and n
1.45
(Israelachvili, 1992a). We obtain for the Hamaker
constant: A 5.2 x10-21 J. Simple calculation shows that
van der Waal attractive forces between hydrate particles
in a oil phase become significant below a distance of the
order of 1 nm (D>1nm
Fa/R<<0.5mN/m). Such a
small distance of separation is unlikely to be achieved
because asphaltenes contained in the crude oil are
expected to adsorb on particles, pushing away particles to
larger distances. Even if we consider that no asphaltenes
are adsorbed, the roughness of particle surface should be
thinner than 1 nanometer, which is difficult to imagine.
Thus, we suggest that, due to adsorption of asphaltenes,
interactions between hydrate particles in the asphaltenic
crude oil may be similar in nature to the ones
encountered
between
polymer-covered
surfaces
(Israelachvili, 1992b): repulsive steric, attractive
intersegment and bridging forces. Such interactions have
been highlighted for crude oils by Christenson and
Israelachvili (1987) with the help of a Surface Forces
Apparatus (S.F.A.). Surface forces were measured
between two cylindrically curved mica surfaces
immersed in an asphaltenic crude oil. The authors
measured forces of attraction in the range: Fa/R
5mN/m to Fa/R 0.5mN/m, associated with hard wall
distances from D 3 nm to D 5 nm. Such forces are
typically of the same order of magnitude as the one we
have determined in the present work.
9. Discussion and Concluding Remarks
In this work we have dealt with hydrate suspensions once
the hydrate formation stage is completely achieved.
Despite no direct observation has been performed, we
propose that asphaltenes adsorbed on the hydrate particle
generate an attraction force between hydrate particles.
The magnitude of this force is of the order: Fa/R
1mN/m. This attraction force leads to a reversible
aggregation process, responsible for the shear thinning
behavior and the thixotropy shown by the suspensions
analyzed.
Van der Waals forces seem to be negligible, even for
nude particles. It would confirm, as frequently reported
by the hydrate community, that hydrate plug formation is
seldom observed once hydrate formation is completed
and hydrate particles are well dispersed in the oil phase.
Thus, as Austvik (1999) reported, “A system in which
most of the water has been converted into hydrates
normally forms a fine powder that is easily transported in
HC liquids”.
On the other hand, the risk of plug formation mainly
occurs during the hydrate formation process.
Consequently, other forces should exist during this stage,
making hydrate particles “sticky”. As a result of the
expected high hydrophilic character of hydrate surface, it
is believed, as suggested by Austvik (1999), that
capillary forces are responsible for the agglomeration
process between hydrate particles. During the hydrate
formation stage, hydrate and liquid water phases co-exist
in the hydrocarbon liquid phase. Water bridges can form
between the hydrate particles, generating attractive
capillary forces. A simple calculation, using the
expression (Israelachvili, 1992c):
Eq. 10 Fa 2 R WO cos
with a contact angle
= 0 (high hydrophilic hydrate
surface) and an interfacial tension WO
10 mN/m,
shows that capillary forces would be of the order: Fa/R >
50 mN/m. This value is quite high when compared with
polymer-like forces (Fa/R 1 mN/m) and van der Waals
0.1 mN/m). Attraction forces of that
forces (Fa/R
magnitude can easily explain plug formation during the
hydrate formation process. Moreover, water bridges may
be converted into hydrate bridges, resulting in a nonreversible aggregation process. Once the hydrate
formation process is completed, there is no longer free
water available to generate capillary forces.
Therefore, wettability properties of hydrate crystals
during the formation process seem to be the dominating
factor concerning plug formation. In the systems
analyzed in the present work the adsorption of
asphaltenes probably made hydrate particles more
hydrophobic, thus preventing the agglomeration process
between particles during the hydrate formation process.
Acknowledgments
This work has been performed within a collaboration
program
involving
IFP,
PETROBRAS
and
TOTALFINAELF. The authors would like to thank these
companies for their financial support and for permission
to publish these results.
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